Thread: matrix algebra

v1 = [1,-3,2] v2 = [-3,9,-6] v3 = [5,-7,h]. For what values of h is v3 in the Span(v1, v2}? For what values of h is {v1,v2,v3} linearly independent?

When I row reduce the matrix, I get 1 -3 5 0
0 0 8 0
0 0 h-10 0

So for when h = 10 the v3 is in the span of v1 and v2?

Originally Posted by lord12

v1 = [1,-3,2] v2 = [-3,9,-6] v3 = [5,-7,h]. For what values of h is v3 in the Span(v1, v2}? For what values of h is {v1,v2,v3} linearly independent?

When I row reduce the matrix, I get 1 -3 5 0
0 0 8 0
0 0 h-10 0

So for when h = 10 the v3 is in the span of v1 and v2?

Did you notice that ? You can use this fact (once you've identified why it's a fact, of course) to answer both questions without even approaching a matrix.